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Connection between graphs and differential equations by Jarvis Pessledale - Tue, 14 Mar 2017 17:17:53 EST ID:ueMHQ1BO No.15418 Ignore Report Quick Reply
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YO WUT IS UP!?
I am curious if anyone knows how to represent differential equations as a graph? I acknowledge that that sounds absurd, but I am curious, I know you can represent a graph via tutte polynomial, so I figured it's not too much of a stretch.
>>
Doris Billingforth - Tue, 14 Mar 2017 17:56:07 EST ID:zpTgkQCY No.15420 Ignore Report Quick Reply
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What do you want exactly? It's not absurd to ask for something as a graph since graphs, like most kinds of mathematical structures, are expressive enough to encode anything you want to do.

A given differential equation will give rise to a dynamical system right? Like if I give you a point the differential equation can tell me the derivative(s) at that point. These derivatives are instantaneous rates of change, but you can imagine for each point in your space following the corresponding tangent vector for a certain time t. If your space is over the reals you will obtain an uncountable family of uncountably infinite combinatorial graphs which vary with t. Maybe you can study the corresponding operators? It looks like the sequence tends to the identity but the way it changes might encode information about your solutions.


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